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P23 [Algebra] - Turkish NMO 1st Round - 2005

Source:

November 2, 2013
ratio

Problem Statement

How many solutions does the equation system x−1xy−3=3−x−y7−x2−y2=y−2xy−4\dfrac{x-1}{xy-3}=\dfrac{3-x-y}{7-x^2-y^2} = \dfrac{y-2}{xy-4} have?
<spanclass=′latex−bold′>(A)</span> 0<spanclass=′latex−bold′>(B)</span> 1<spanclass=′latex−bold′>(C)</span> 2<spanclass=′latex−bold′>(D)</span> 3<spanclass=′latex−bold′>(E)</span> 4 <span class='latex-bold'>(A)</span>\ 0 \qquad<span class='latex-bold'>(B)</span>\ 1 \qquad<span class='latex-bold'>(C)</span>\ 2 \qquad<span class='latex-bold'>(D)</span>\ 3 \qquad<span class='latex-bold'>(E)</span>\ 4
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